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A Constructive Proof of Ky Fan's Generalization of Tucker's Lemma

Timothy Prescott, Francis Edward Su

Published 2003-10-28Version 1

We present a constructive proof of Ky Fan's combinatorial lemma concerning labellings of triangulated spheres. Our construction works for triangulations of $S^n$ that contain a flag of hemispheres. As a consequence, we produce a constructive proof of Tucker's lemma that holds for a larger class of triangulations than previous constructive proofs.

Comments: related work at http://www.math.hmc.edu/~su/papers.html
Journal: J. Combin. Theory Ser. A 111 (2005), 257--265
Categories: math.CO, math.AT
Subjects: 55M20, 05A99, 52B70
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